How correlation works
Everything the game is testing, in one place.
What r can't tell you
A high r is not proof of much on its own. These four plots all score around +0.8.
The lesson: always look at the plot. r is a summary, and every summary throws something away.
Beyond Pearson's r
Pearson's r isn't the only number worth looking at.
Spearman's rank correlation
Spearman ranks the values first, then correlates the ranks.
Neither is "the right one" — they answer different questions.
What a p-value does and doesn't mean
A p-value asks: if there were no real relationship, how often would chance alone produce a correlation this strong?
The same correlation, at different sample sizes:
Significant does not mean strong
With enough data, almost any tiny correlation becomes "significant".